Transverse correlations in the inhomogeneous one-dimensional XY-model at infinite temperature

Perk, Jacques H. H.; Capel, H.W.

doi:10.1016/0378-4371(78)90026-2

Cited by 40 publications

(8 citation statements)

References 41 publications

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“…In this limit, the xx and xy time-dependent spin correlations at different sites vanish and only the autocorrelations survive, s x n (t)s x n+m | J = (1/4) cos(ht) exp − J2 t 2 /4 δ m,0 , s x n (t)s y n+m | J = (1/4) sin(ht) exp − J2 t 2 /4 δ m,0 (in that case (i.e. when only autocorrelations survive) according to (3) we have simply s x n (t)s x n+m | J,D = s x n (t)s x n+m | J and s x n (t)s y n+m | J,D = s x n (t)s y n+m | J ; this result for the model (1), which follows by symmetry from the results for the model ( 4), was also derived earlier by direct calculation [20] (see Eq. (4.8) of that paper)).…”

Section: Zz Dynamic Structure Factorsupporting

confidence: 79%

“…In the present paper, we employ the Jordan-Wigner fermionization supplemented by further analytical and numerical calculations to perform a comprehensive analysis of the effect of the Dzyaloshinskii-Moriya interaction on the dynamic structure factors of the spin-1/2 XX chain in a transverse field. The previous studies of the effect of the Dzyaloshinskii-Moriya interaction were restricted to transverse (zz) dynamics [18,19] and to the dynamics of correlations between x and y spin components at infinite temperature [20].…”

Section: Introductory Remarksmentioning

confidence: 99%

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Dynamic Structure Factors of the Spin-1/2XXChain with Dzyaloshinskii–Moriya Interaction

Derzhko

Verkholyak

2006

J. Phys. Soc. Jpn.

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We consider the spin-1/2 isotropic XY chain in a (z) transverse magnetic field with the Dzyaloshinskii-Moriya interaction directed along the z-axis in spin space and examine the effects of the latter interaction on the zz, xx (yy) and xy (yx) dynamic structure factors. The Dzyaloshinskii-Moriya interaction does not manifest itself in the zz dynamic quantities. In contrast, the xx (yy) and xy (yx) dynamic structure factors show dramatical changes owing to the Dzyaloshinskii-Moriya interaction. Implications of our results for electron spin resonance experiments are briefly discussed. PACS number(s): 75.10.-b

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Section: Zz Dynamic Structure Factorsupporting

confidence: 79%

Section: Introductory Remarksmentioning

confidence: 99%

Dynamic Structure Factors of the Spin-1/2XXChain with Dzyaloshinskii–Moriya Interaction

Derzhko

Verkholyak

2006

J. Phys. Soc. Jpn.

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“…The auto-correlation functions of this model have been found analytically in the infinite temperature limit [19], and the time dependent σ z l (t)σ z l+R has been found, also analytically, for arbitrary temperature [20]. However, the general equilibrium correlation functions have not been calculated previously.…”

Section: Correlation Functionsmentioning

confidence: 96%

Entanglement and the interplay between staggered fields and couplings

2012

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We investigate how the interplay between a staggered magnetic field and staggered coupling strength affects both ground state and thermal entanglement. Upon analytically calculating thermodynamic quantities and the correlation functions for such a system, we consider both the global Meyer-Wallach measure of entanglement and the concurrence between pairs of spins. We discover two quantum phase transitions present in the model and show that the quantum phase transitions are reflected in the behaviour of the entanglement at zero temperature. We discover that increasing the alternating field and alternating coupling strength can actually increase the amount of entanglement present at both zero temperature and for thermal states of the system.

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“…3 The case of finite temperature should work out fine also according to a calculation we have done with approximate initial conditions, utilizing the exponential decay with separation in the initial conditions. The case of infinite temperature has been studied before in great detail [16,17,18,19,20,21,22,23]. We shall use some of the older results for zero temperature [11,24,25,26,27,28,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

Perk

Au-Yang

2009

J Stat Phys

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In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent paircorrelations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.

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Transverse correlations in the inhomogeneous one-dimensional XY-model at infinite temperature

Cited by 40 publications

References 41 publications

Dynamic Structure Factors of the Spin-1/2XXChain with Dzyaloshinskii–Moriya Interaction

Dynamic Structure Factors of the Spin-1/2XXChain with Dzyaloshinskii–Moriya Interaction

Entanglement and the interplay between staggered fields and couplings

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

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